Please help me verify this identity? tan(x + pi/4) = (cosx + sinx)/(cosx - sinx)?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to prove that tan(x + pi/4) = (cos x + sin x)/(cos x - sin x)

We know that tan (a + b) = [tan a + tan b]/(1 - tan a * tan b)

tan(x + pi/4)

=> (tan x + tan pi/4) / (1 - tan x * tan pi/4)

tan pi/4 = 1

=> (tan x + 1) / ( 1 - tan x)

=> [(sin x / cos x) + 1]/[1 - (sin x / cos x)]

=> [(sin x + cos x)/cos x]/ [(cos x - sin x)/cos x]

=> (sin x + cos x)/ (cos x - sin x)

This proves that tan(x + pi/4)= (cos x + sin x)/(cos x - sin x)

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